# Torque Self-Test: The Right Hand Rule

Recall  $\tau = r\times F = r F \sin \theta$

In both diagrams (parts a and b), the force vector F can be thought of as having acted on the arrowhead of moment arm r. However, F has been translated (moved) so that the two vectors are tail-to-tail. This was done in order to simplify the problem.

## Part A

In the following diagram, use the right hand rule to find the direction of torque. The direction of torque is:

• A. into the screen
• B. out of the screen
• C. to the left
• D. to the right
• E. upwards
• F. downwards

• A. No. The tourque cannot be in the plane of the other two vectors.
• B. Correct
• C. No. The tourque cannot be in the plane of the other two vectors.
• D. No. The tourque cannot be in the plane of the other two vectors.
• E. No. The tourque cannot be in the plane of the other two vectors.
• F. No. The tourque cannot be in the plane of the other two vectors.

## Part B

In the following diagram, in which direction is the torque? The direction of torque is:

• A. into the screen
• B. out of the screen
• C. to the left
• D. to the right
• E. upwards
• F. downwards

• A. Correct
• B. No. Remember it is F rotated into r.
• C. No. The tourque cannot be in the plane of the other two vectors.
• D. No. The tourque cannot be in the plane of the other two vectors.
• E. No. The tourque cannot be in the plane of the other two vectors.
• F. No. The tourque cannot be in the plane of the other two vectors.

#### Solution

Recall that  = r x F, (or  = r F sin) and that the Right Hand Rule says that the thumb points into the direction of torque  when the fingers curl in the direction of the cross product (ie. from r to F). Furthermore, the symbol  represents a vector going into the screen, while  is a vector pointing out of the screen.

## Part A In the first problem, you would point your fingers in the direction of r (left-ward), and 'curl' them upwards (into the direction of F). Your thumb should point into the screen. (Be sure you are using your right hand.)

## Part B In the second problem, r points to the right, so point your fingers to the right. Now 'curl' them upwards, in the direction of F. Your thumb should point out of the screen.